{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:KAWTXFXL7EAUXQJINNPH24M7EB","short_pith_number":"pith:KAWTXFXL","schema_version":"1.0","canonical_sha256":"502d3b96ebf9014bc1286b5e7d719f2058b7d6e8b4f2fb2f361bc372cdaf2f26","source":{"kind":"arxiv","id":"2606.10748","version":1},"attestation_state":"computed","paper":{"title":"Fr\\'echet Means of Periodic Orbits in Dynamical Systems: Geometry, Dynamics, and Diagnostics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Christian Kuehn, Paulina Hering","submitted_at":"2026-06-09T11:58:59Z","abstract_excerpt":"In many dynamical systems applications, one seeks representative trajectories summarizing families of periodic orbits arising from parameter variation or uncertainty. While the Fr\\'echet mean provides a natural notion of averaging in nonlinear metric spaces, its application to periodic trajectories is complicated by the interplay between geometric shape and temporal dynamics. Inspired by ideas from shape analysis, we develop a framework for computing Fr\\'echet means of periodic orbits by representing trajectories as closed curves and introducing a metric structure on a quotient space that acco"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2606.10748","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2026-06-09T11:58:59Z","cross_cats_sorted":[],"title_canon_sha256":"15990965fa0ed41cb935b3ddc4f1472e42c99be0bca6dfe0ded8d67b9e165e3c","abstract_canon_sha256":"fe0f91a3fc5efceb151acc7237a2bf36a52236461dd08325ab74b465a1d85234"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-10T01:10:38.253852Z","signature_b64":"GxLnsDF9ZpBY5X9fKuw7v3Sos6uGYuaOKNHAyd8fiaWD9J9WXK/gY/Yaxl2dL/P3blrkE5wnPhB49yQnUka0CQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"502d3b96ebf9014bc1286b5e7d719f2058b7d6e8b4f2fb2f361bc372cdaf2f26","last_reissued_at":"2026-06-10T01:10:38.253009Z","signature_status":"signed_v1","first_computed_at":"2026-06-10T01:10:38.253009Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Fr\\'echet Means of Periodic Orbits in Dynamical Systems: Geometry, Dynamics, and Diagnostics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Christian Kuehn, Paulina Hering","submitted_at":"2026-06-09T11:58:59Z","abstract_excerpt":"In many dynamical systems applications, one seeks representative trajectories summarizing families of periodic orbits arising from parameter variation or uncertainty. While the Fr\\'echet mean provides a natural notion of averaging in nonlinear metric spaces, its application to periodic trajectories is complicated by the interplay between geometric shape and temporal dynamics. Inspired by ideas from shape analysis, we develop a framework for computing Fr\\'echet means of periodic orbits by representing trajectories as closed curves and introducing a metric structure on a quotient space that acco"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.10748","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2606.10748/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"2606.10748","created_at":"2026-06-10T01:10:38.253147+00:00"},{"alias_kind":"arxiv_version","alias_value":"2606.10748v1","created_at":"2026-06-10T01:10:38.253147+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.10748","created_at":"2026-06-10T01:10:38.253147+00:00"},{"alias_kind":"pith_short_12","alias_value":"KAWTXFXL7EAU","created_at":"2026-06-10T01:10:38.253147+00:00"},{"alias_kind":"pith_short_16","alias_value":"KAWTXFXL7EAUXQJI","created_at":"2026-06-10T01:10:38.253147+00:00"},{"alias_kind":"pith_short_8","alias_value":"KAWTXFXL","created_at":"2026-06-10T01:10:38.253147+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/KAWTXFXL7EAUXQJINNPH24M7EB","json":"https://pith.science/pith/KAWTXFXL7EAUXQJINNPH24M7EB.json","graph_json":"https://pith.science/api/pith-number/KAWTXFXL7EAUXQJINNPH24M7EB/graph.json","events_json":"https://pith.science/api/pith-number/KAWTXFXL7EAUXQJINNPH24M7EB/events.json","paper":"https://pith.science/paper/KAWTXFXL"},"agent_actions":{"view_html":"https://pith.science/pith/KAWTXFXL7EAUXQJINNPH24M7EB","download_json":"https://pith.science/pith/KAWTXFXL7EAUXQJINNPH24M7EB.json","view_paper":"https://pith.science/paper/KAWTXFXL","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2606.10748&json=true","fetch_graph":"https://pith.science/api/pith-number/KAWTXFXL7EAUXQJINNPH24M7EB/graph.json","fetch_events":"https://pith.science/api/pith-number/KAWTXFXL7EAUXQJINNPH24M7EB/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/KAWTXFXL7EAUXQJINNPH24M7EB/action/timestamp_anchor","attest_storage":"https://pith.science/pith/KAWTXFXL7EAUXQJINNPH24M7EB/action/storage_attestation","attest_author":"https://pith.science/pith/KAWTXFXL7EAUXQJINNPH24M7EB/action/author_attestation","sign_citation":"https://pith.science/pith/KAWTXFXL7EAUXQJINNPH24M7EB/action/citation_signature","submit_replication":"https://pith.science/pith/KAWTXFXL7EAUXQJINNPH24M7EB/action/replication_record"}},"created_at":"2026-06-10T01:10:38.253147+00:00","updated_at":"2026-06-10T01:10:38.253147+00:00"}